A new, systematic approach to the synthesis of Cartesian stiffness by springs is presented using screw (spatial vector) algebra. The space of solutions is fully characterized for all stiffnesses realizable by springs. The main result shows that a rank r stiffness can always be synthesized by r springs. Further, it can also be synthesized by an arbitrarily large number of springs greater than r. Synthesis algorithms are presented and numerical results support the theory.

Remote center-of-compliance devices have long been used to facilitate insertion for assembly operations. A new analysis with a more accurate model better characterizes the interesting properties of remote compliance. The center location and stiffiness are presented as nondimensional ratios that are functions of geometrical properties. New results describe: i) the high sensitivity of the center location and ii) the inverse relationship between linear and angular lateral stiffnesses.